Actively maintaining system frequency and voltage, grid-forming (GFM) inverters that embed a synchronous machine emulation may exhibit interactions with other voltage sources in the grid, leading to poorly-damped power oscillations. To enhance the damping of oscillations, massive studies have been conducted. However, the existing solutions are sometimes implicitly equivalent to one another or mainly concentrate on a single performance aspect of GFM control. In this article, a generic control scheme capable of incorporate established GFM controls is first proposed. Afterwards, two design approaches are developed, simultaneously considering main performance aspects of GFM control: reference tracking, disturbance damping, and inertial response. Employing the developed control scheme with design approaches, three main performance aspects can be quantitatively evaluated in sequence while maintaining explicit relationships with their own indexes. Finally, experimental results from a 2.2 kW GFM inverter have validated the effectiveness of the active-damping controls, design approaches, and theoretical analyses presented in this study.